Complexity of the Guided Local Hamiltonian Problem: Improved Parameters and Extension to Excited States

Recently it was shown that the so-called guided local Hamiltonian problem -- estimating the smallest eigenvalue of a $k$-local Hamiltonian when provided with a description of a quantum state ('guiding state') that is guaranteed to have substantial overlap with the true groundstate -- is BQP-complete for $k \geq 6$ when the required precision is inverse polynomial in the system size $n$, and remains hard even when the overlap of the guiding state with the groundstate is close to a constant $\left(\frac12 - \Omega\left(\frac{1}{\mathop{poly}(n)}\right)\right)$. We improve upon this result in three ways: by showing that it remains BQP-complete when i) the Hamiltonian is 2-local, ii) the overlap between the guiding state and target eigenstate is as large as $1 - \Omega\left(\frac{1}{\mathop{poly}(n)}\right)$, and iii) when one is interested in estimating energies of excited states, rather than just the groundstate. Interestingly, iii) is only made possible by first showing that ii) holds.Comment: 22 pages, 3 figure

Guidable Local Hamiltonian Problems with Implications to Heuristic Ans\"atze State Preparation and the Quantum PCP Conjecture

We study 'Merlinized' versions of the recently defined Guided Local Hamiltonian problem, which we call 'Guidable Local Hamiltonian' problems. Unlike their guided counterparts, these problems do not have a guiding state provided as a part of the input, but merely come with the promise that one exists. We consider in particular two classes of guiding states: those that can be prepared efficiently by a quantum circuit; and those belonging to a class of quantum states we call classically evaluatable, for which it is possible to efficiently compute expectation values of local observables classically. We show that guidable local Hamiltonian problems for both classes of guiding states are $\mathsf{QCMA}$-complete in the inverse-polynomial precision setting, but lie within $\mathsf{NP}$ (or $\mathsf{NqP}$) in the constant precision regime when the guiding state is classically evaluatable. Our completeness results show that, from a complexity-theoretic perspective, classical Ans\"atze selected by classical heuristics are just as powerful as quantum Ans\"atze prepared by quantum heuristics, as long as one has access to quantum phase estimation. In relation to the quantum PCP conjecture, we (i) define a complexity class capturing quantum-classical probabilistically checkable proof systems and show that it is contained in $\mathsf{BQP}^{\mathsf{NP}[1]}$ for constant proof queries; (ii) give a no-go result on 'dequantizing' the known quantum reduction which maps a $\mathsf{QPCP}$-verification circuit to a local Hamiltonian with constant promise gap; (iii) give several no-go results for the existence of quantum gap amplification procedures that preserve certain ground state properties; and (iv) propose two conjectures that can be viewed as stronger versions of the NLTS theorem. Finally, we show that many of our results can be directly modified to obtain similar results for the class $\mathsf{MA}$.Comment: 61 pages, 6 figure

Do ether functionalized ionic liquids improve the CO2 solubility?

CO2 absorption using a solvent is accepted as the most compatible technology. In the recent years ionic liquids (ILs) have shown to be good candidates for CO2 capture. They exhibit major advantages compared to amine-based systems. Their negligible vapor pressure, high thermal and chemical stability and tunability outweigh the disadvantages of lower absorptive capacity and kinetics. In this work a comprehensive study of the ILs [C2mim]-, [C4mim]-, [C6mim]-, [C7mim]- and [C8mim] tricyanomethanide (TCM) has been carried out. Furthermore, in order to evaluate the presence of ether groups in the alkyl chain of the imidazolium, this work includes 1-(2-methoxythyl)-3-methylimidazolium- and 1[2-(2- methoxyethoxy)ethyl]-3-methylimidazolium tricyanomethanide. These non-flourinated and low-viscous ILs are studied for the first time as a solvent for CO2 capture. Two different methods (volumetric vs gravimetric) were applied to study the thermodynamics (i.e., absorptive capacity and Henry’s law coefficient) and kinetics (i.e., diffusion coefficient) at several temperatures and pressures up to 150 bars. The experimentally determined phase behavior of the IL and CO2 systems are correlated using the Peng-Robinson equation of state. Furthermore, the thermal operating window (e.g., glass transition and decomposition temperature) and physical properties (e.g., density, viscosity, conductivity and surface tension) were determined. It will be shown at the conference that TCM-based ILs are promising sorbents for pre-combustion CO2 capture due to their high (physical) absorptive capacity, their low regeneration energy consumption (low heat of absorption) and improved kinetics (due to their low viscosity) compared to the conventional ILs

Optimized Trigger for Ultra-High-Energy Cosmic-Ray and Neutrino Observations with the Low Frequency Radio Array

When an ultra-high energy neutrino or cosmic ray strikes the Lunar surface a radio-frequency pulse is emitted. We plan to use the LOFAR radio telescope to detect these pulses. In this work we propose an efficient trigger implementation for LOFAR optimized for the observation of short radio pulses.Comment: Submitted to Nuclear Instruments and Methods in Physics Research Section

Finding quantum partial assignments by search-to-decision reductions

In computer science, many search problems are reducible to decision problems, which implies that finding a solution is as hard as deciding whether a solution exists. A quantum analogue of search-to-decision reductions would be to ask whether a quantum algorithm with access to a $\mathsf{QMA}$ oracle can construct $\mathsf{QMA}$ witnesses as quantum states. By a result from Irani, Natarajan, Nirkhe, Rao, and Yuen (CCC '22), it is known that this does not hold relative to a quantum oracle, unlike the cases of $\mathsf{NP}$, $\mathsf{MA}$, and $\mathsf{QCMA}$ where search-to-decision relativizes. We prove that if one is not interested in the quantum witness as a quantum state but only in terms of its partial assignments, i.e. the reduced density matrices, then there exists a classical polynomial-time algorithm with access to a $\mathsf{QMA}$ oracle that outputs approximations of the density matrices of a near-optimal quantum witness, for any desired constant locality and inverse polynomial error. Our construction is based on a circuit-to-Hamiltonian mapping that approximately preserves near-optimal $\mathsf{QMA}$ witnesses and a new $\mathsf{QMA}$-complete problem, Low-energy Density Matrix Verification, which is called by the $\mathsf{QMA}$ oracle to adaptively construct approximately consistent density matrices of a low-energy state.Comment: 20 page

Genetic disposition and response of blood lipids to diet : studies on gene-diet interaction in humans

Even though a cholesterol-lowering diet is effective for most people, it is not for all. Identification of genetic determinants of the serum lipid response to diet may be of help in the identification of subjects who will not benefit from a cholesterol-lowering diet. It may also clarify the role of certain proteins in cholesterol metabolism. The objective of our research was to determine whether genetic polymorphisms affect the response of serum lipids to diet in humans.We first assessed sex differences in the response of serum lipids to changes in the diet. Men had larger responses of total and low-density lipoprotein cholesterol to saturated fat and cafestol than women. There were no sex differences in the responses to trans fat and dietary cholesterol. We also used these data to study the effect of 11 genetic polymorphisms on responses of serum lipids to the various dietary treatments. Apoprotein E, A4 347 and 360, and cholesteryl-ester transfer protein TaqIb polymorphisms affected the lipid response to diet slightly.We further studied the effect of the apoprotein A4 360-1/2 polymorphism on response of serum lipids to dietary cholesterol in a controlled trial specially designed for this purpose. The apoprotein A4 360-1/2 polymorphism did not affect the response of serum lipids to a change in the intake of cholesterol in a group of healthy Dutch subjects who consumed a background diet high in saturated fat.Although it is not directly related to genetic polymorphisms and lipid response, we finally reviewed the effect of dietary cholesterol on the ratio of total to high-density lipoprotein cholesterol, which is a more specific predictor of coronary heart disease than either lipid value alone. Dietary cholesterol raised the ratio of total to high-density lipoprotein cholesterol.In conclusion, the effect of genetic polymorphisms on serum lipid response to diet is small. It is therefore not possible to identify individuals who will not benefit from a cholesterol-lowering diet on the basis of a specific genetic polymorphism.</p

Computer says no: understanding digital authority

"Computer Says No" is a philosophical exploration of the mechanisms behind people’s willingness tostrongly rely on digital technologies for decision-making. It describes the growing role of algorithms in modern societies, and the potential implications of overly trusting and respecting machines. This dissertation coins the idea of digital authority to reflect on this compelling influence of modern technologies on human thoughts and actions – highlighting that they can be much more than tools or assistants for improved decision-making. Rather, in today’s world, technologies have become potential authorities that we may come to follow upon. The aim of this book is to provide readers with a nuanced understanding of digital authority that will also allow for the development of effective and ethical solutions for the serious problems that can arise from our blind reliance on digital technologies.Security and Global Affair

Permutation tests for quantum state identity

The quantum analogue of the equality function, known as the quantum state identity problem, is the task of deciding whether $n$ unknown quantum states are equal or unequal, given the promise that all states are either pairwise orthogonal or identical. Under the one-sided error requirement, it is known that the permutation test is optimal for this task, and for two input states this coincides with the well-known Swap test. Until now, the optimal measurement in the general two-sided error regime was unknown. Under more specific promises, the problem can be solved approximately or even optimally with simpler tests, such as the circle test. This work attempts to capture the underlying structure of (fine-grained formulations of) the quantum state identity problem. Using tools from semi-definite programming and representation theory, we (i) give an optimal test for any input distribution without the one-sided error requirement by writing the problem as an SDP, giving the exact solutions to the primal and dual programs and showing that the two values coincide; (ii) propose a general $G$-test which uses an arbitrary subgroup $G$ of $\text{S}_n$, giving an analytic expression of the performance of the specific test, and (iii) give an approximation of the permutation test using only a classical permutation and $n-1$ Swap tests.Comment: 15 pages, 1 figur